A Robust Generalised Fuzzy c-Means Clustering Algorithm with Local Spatial Information

Abstract

Data clustering have been used as useful tool in many pattern recognition and computer vision applications. This dissertation reviews partitional clustering approaches to classify the data. It is well-known that clustering the data affected by the outliers and noise can be very harmful in many computer vision and pattern recognition applications. In order to overcome the noise, many partitional clustering methods have been proposed in the last decade. Mostly the perfect information cannot be obtained from any type of data in data analysis applications. Fuzzy c-Means Clustering (FMC) algorithms is able to retain more knowledge or information from original data set comparatively than hard or crisp clustering algorithms but still FCM needs more local information to be retained in order to make it more robust to noise and outliers, and to improve its clustering performance. This dissertation deals with incorporating the local information in FCM clustering. In the last decade, much research has been conducted on fuzzy c-means (FCM) clustering algorithms for image segmentation that incorporate the local neighborhood information into their objective function in order to deal with the images corrupted by noise and outliers. Although the bias-corrected fuzzy c-means (BCFCM), FCM with spatial constraints (FCM_S1), and adaptive weighted averaging (FCM_AWA) algorithms have proven to be robust to noise for image segmentation using local spatial image information, but they have some disadvantages: (1) they are limited to one-dimensional input data i.e. images (Intensity Level feature used as one dimension), (2) their robustness to noise and effectiveness heavily depend on a crucial parameter α, and (3) it is difficult to find the optimal value of α, which is generally selected experimentally. Among these image segmentation methods incorporating local neighborhood information of pixels, Kernel weighted Fuzzy Local Information C-Means (KWFLICM) algorithm has proven more robust even for the images that were contaminated by high frequency noise. The disadvantage of KWFLICM is that limitation of applicable to one dimensional input data i.e. images (Intensity Level feature used as one dimension). Since the one dimensional data or image data is ordered, where the neighbors of a pixel can be determined by applying the square window around that pixel. However, for M-dimensional data e.g. sonar data set with 60 features etc. it is unknown which data vectors are neighbors to each other. In this dissertation we purpose the two different methods of finding the neighbors for M-dimensional input data. We purpose generalize the adaptive weighted averaging (FCM_AWA) algorithm by applying one method of neighbors finding so that it can be applicable to any number of dimensional input data. Generalized FCM_AWA is named Generalised Fuzzy c-Means clustering algorithm with Information (GFCMLI) which overcomes above mentioned disadvantages of FCM_AWA. We also propose a generalization of KWFLICM (GKWFLICM) that is applicable to M-dimensional input data sets by applying second method of neighbor finding. The proposed generalized methods not only mitigates the disadvantages of standard FCM clustering algorithm FCM (sensitive to noise and outliers, poor performance for clusters with different sizes and for clusters with different density) but also highly improves the overall clustering performance. Experiments have been performed on several noisy data sets and natural/real-world images in order to demonstrate the effectiveness, efficiency, and robustness to noise of our proposed methods algorithm as compared to conventional methods.